Yes, but we can still be confident in the broad pattern. Paul Romer explains:
My conviction that the rate of growth in GDP per capita at the technological frontier had to be increasing over time sprang from a simple calculation. Suppose the modern rate of growth of real GDP per capita (that is the growth rate after taking out the effects of inflation) is equal to 2% per year and that income per capita in year 2000 is $40,000. If this rate had prevailed for the last 1,000 years, then in the year 1000, income per capita measured in the purchasing power of dollars today would have been $0.0001, or 0.01 cents. This is way too small to sustain life. If the growth rate had been falling over time instead of remaining constant, then the implied measure of GDP per capita in the year 1000 would have been even lower.
He concludes:
Reasonable people can differ about what the future holds, but the simple calculation that first got me thinking about this (and which no doubt influenced how Maddison did the backward projections to come up with his estimates) leaves no room for doubt about what happened in the past. The rate of growth of GDP per capita has increased over time.
GDP per capita is growing ~linear on a logarithmic scale though:
https://ourworldindata.org/economic-growth
Over the last ~150 years, yes, but not over much longer timescales.
Any data we have on GDP per capita in the 18th century is probably dubious. In the 10th century ? Not even dubious.
Yes, but we can still be confident in the broad pattern. Paul Romer explains:
He concludes: